You can collect the castings and spread them on a canvas tarp (plastic ones don't work for this, for me at least) to allow the excess moisture a way to leave.
I generally let this sit out for a day, I might walk by and use the tarp corners to move the castings around so the damp ones next to the tarp are exposed to some fresh air or I might forget to do this, overall it doesn't really seem to matter much.
Once they aren't dripping moisture I move them from the tarp to some news print paper that is easier to manipulate into a funnel shape so I can put them into empty
feed sacks for storage. (I use feed bags because I have lots of them all the time, they also let some air pass through but most bugs can't get in.)
I don't want the castings to completely dry out because the dust from them can be irritating to lungs, eyes and throat.
I haven't stored them very long but I know two market farmers that have some that are two years old and still in good shape in their feed bag storage system. (these guys have mentioned that the castings are good up to three years stored this way, mine are gone in just under a year so I have no personal experience with longer term storage of castings, I do feel like they are good, honest folks though and I trust what they told me about their own worm farming businesses).